Related papers: Quadratic functors and one-connected two stage spa…

We present a ``hierarchical'' strategy for phase space generation in order to efficiently map the antenna momentum structures, typically occurring in QCD amplitudes.

A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…

In this paper, a class of fractals, called quadrilateral labyrinth fractals, are introduced and studied. They are a special kind of fractals on any quadrilateral on the plane. This type of fractal is motivated by labyrinth fractal on the…

We investigate the topological classification of excitations in quadratic bosonic systems with an excitation band gap. Time-reversal, charge-conjugation, and parity symmetries in bosonic systems are introduced to realize a ten-fold symmetry…

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…

Quantum fluctuation and quantum entanglement of the pump field reflected from an optical cavity for type II second harmonic generation are theoretically analyzed. The correlation spectra between the quadratures of the reflected subharmonic…

In previous work, we defined the category of functors Fquad, associated to vector spaces over the field with two elements equipped with a nondegenerate quadratic form. In this paper, we define a special family of objects in the category…

In this paper, we study the moduli spaces of parabolic connections with a quadratic differential. We endow these moduli spaces with symplectic structures by using the fundamental 2-forms on the moduli spaces of parabolic connections (which…

The 1-D dimension harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. In the…

The paper is devoted to the study of homotopy properties of stabilizers of smooth functions on oriented surfaces, i.e., groups of diffeomorphisms of surfaces preserving a given function. For some class of smooth functions which is a…

Function space topologies are developed for EC(Y,Z), the class of equi-continuous mappings from a topological space Y to a uniform space Z. Properties such as splittingness, admissibility etc. are defined for such spaces. The net theoretic…

For any object A in a simplicial model category M, we construct a topological space \^A which classifies homogeneous functors whose value on k open balls is equivalent to A. This extends a classification result of Weiss for homogeneous…

We consider two categories related to symplectic manifolds: 1. Objects are symplectic manifolds and morphisms are symplectic embeddings. 2. Objects are symplectic manifolds endowed with compatible almost complex structure and morphisms are…

We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain…

The systems with multimode nonstationary Hamiltonians quadratic in position and momentum operators are reviewed. The tomographic probability distributions (tomograms) for the Fock states and Gaussian states of the quadratic systems are…

We present a new class of quantum phase transitions that refer neither to local order parameter and critical fluctuations nor to continuous symmetry breaking but are assigned by the step-wise change in topology of the multi-particle system…

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…

We introduce the homotopy surface category of a space which generalizes the 1+1-dimensional cobordism category of circles and surfaces to the situation where one introduces a background space. We explain how for a simply connected…

We consider various two-leg ladder models exhibiting gapped phases. All of these phases have short-ranged valence bond ground states, and they all exhibit string order. However, we show that short-ranged valence bond ground states divide…

We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modules over small preadditive categories. The second is with…